Most newspapers round the world have online editions as well. While you get the news, you don't get to see things like Classifieds, Seasonal Sales etc.,. Some newspapers offer a digital edition of the "print" version which can be useful if you need such info and you missed a copy. You also get to choose local edition of different regions. So if you have re-located to a new city, you can still track news of you home city. Here is a compilation of the popular newspapers in Hyderabad (where I stay) & India:
Deccan Chronicle (free, registration required)
Times of India
Hindustan Times (free, registration required)
Indian Express (free, registration required)
Economic Times
Business Standard (free, registration required)
Eenadu (free, registration required)
Sakshi
Also see:
Beat the Recession with Tip Jar